A Generalized Non-Uniform Rational B-Spline Framework with Global G^2 Continuity

A method for constructing globally G^2-continuous spline surfaces over control meshes with extraordinary points (EPs) is proposed in this paper. For each control mesh face that is not adjacent to EPs, a bicubic B\'ezier patch is generated, whereas each patch within the 1-ring neighborhood of an EP is subdivided into four subpatches, each of which is assigned a biquintic B\'ezier patch. Furthermore, we introduce a novel auxiliary control point (anchor) scheme exclusively for sharp EPs to fundamentally overcome the inherent deficiency of the generalized non-uniform rational B-spline (G-NURBS) framework in accurately modeling sharp features at singular points. G^2-continuity conditions are enforced at shared patch boundaries by optimizing the positions of the B\'ezier control points. The experimental results not only validate the effectiveness of the method in achieving global G^2-continuity near EPs but also, through comparative studies with existing methods, demonstrate its superior geometric fidelity and high-accuracy reconstruction of computer-aided design (CAD) models that contain sharp features. The hybrid patch configuration, combined with a stepwise optimization strategy and the improved sharp feature modeling ability, effectively addresses continuity and fidelity challenges that arise from arbitrary topological meshes.